SOLUTION: Hi outstanding tutors, I cannot figure out how to set up this linear word problem. I do;t even know how to begin. Here is the problem: You are driving to a concert. To arrive on

Question 970255: Hi outstanding tutors,
I cannot figure out how to set up this linear word problem. I do;t even know how to begin. Here is the problem:
You are driving to a concert. To arrive on time, you plan to travel at an average speed of 45 miles per hour. For the first two hours of the trip you travel at 40 miles per hour. Find the expression for the total time you traveled. Then use the following verbal models to find how many hours you traveled at 55 miles per hour to arrive on time.
Distance at 40mi/hr + distance at 55 mi/hr = Total distance
Average speed * Total time = Total distance
Thank you for taking time to work this!
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
ANSWER 1:
T=Total time=Total distance/45mph=Time at 40mph + Time at 55 mph
.
Distance at 40mi/hr + distance at 55 mi/hr = Total distance
Distance at 40mph=40mph(2hrs)=80 mi
Let T=total time
Total distance=(45mph)(T)
Time at 55mph=T-time at 40mph=T-2 hrs
Distance at 55mph=(55mph)(T-2 hrs)
80mi+(55mph)(T-2 hrs)=45mph(T)
80mi+55mph(T)-110mi=45mph(T)
55mph(T)-30mi=45mph(T) Subtract 55mph(T) from each side
-30mi=-10mph(T) Divide each side by -10mph
3 hours=T The total time was 3 hours
.
Time at 55 mph=T-2hrs=3 hrs-2 hrs=1 hr
ANSWER 2: You traveled 1 hour at 55 mph
.
CHECK:
Distance at 40mi/hr + distance at 55 mi/hr = Total distance
(40mph)(2hr)+(55mph)(1hr)=(45mph)(3hr)
80mi+55mi=135mi
135mi=135mi
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